TY - JOUR

T1 - Controlling the local false discovery rate in the adaptive Lasso

AU - Sampson, J. N.

AU - Chatterjee, N.

AU - Carroll, R. J.

AU - Muller, S.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Sampson's and Chatterjee's research was supported by the Intramural Research Program of the NCI. Chatterjee's research was supported by a gene-environment initiative grant from the NHLBI (RO1-HL091172-01). Muller's research was supported by a grant from the Australian Research Council (DP110101998). Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). Carroll was also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/4/9

Y1 - 2013/4/9

N2 - The Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of "false positives" in practice. Here, we adapt the concept of local false discovery rates (lFDRs) so that it applies to the sequence, λn, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given λn to be the probability that the variable added to the model by decreasing λn to λn-δ is not associated with the outcome, where δ is a small value. We derive the relationship between the lFDR and λn, show lFDR =1 for traditional smoothing parameters, and show how to select λn so as to achieve a desired lFDR. We compare the smoothing parameters chosen to achieve a specified lFDR and those chosen to achieve the oracle properties, as well as their resulting estimates for model coefficients, with both simulation and an example from a genetic study of prostate specific antigen.

AB - The Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of "false positives" in practice. Here, we adapt the concept of local false discovery rates (lFDRs) so that it applies to the sequence, λn, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given λn to be the probability that the variable added to the model by decreasing λn to λn-δ is not associated with the outcome, where δ is a small value. We derive the relationship between the lFDR and λn, show lFDR =1 for traditional smoothing parameters, and show how to select λn so as to achieve a desired lFDR. We compare the smoothing parameters chosen to achieve a specified lFDR and those chosen to achieve the oracle properties, as well as their resulting estimates for model coefficients, with both simulation and an example from a genetic study of prostate specific antigen.

UR - http://hdl.handle.net/10754/597869

UR - https://academic.oup.com/biostatistics/article-lookup/doi/10.1093/biostatistics/kxt008

UR - http://www.scopus.com/inward/record.url?scp=84888382617&partnerID=8YFLogxK

U2 - 10.1093/biostatistics/kxt008

DO - 10.1093/biostatistics/kxt008

M3 - Article

C2 - 23575212

VL - 14

SP - 653

EP - 666

JO - Biostatistics

JF - Biostatistics

SN - 1465-4644

IS - 4

ER -